Fast Fourier transform (FFT) signal analyzers are well known in the art, as shown by U.S. Pat. Nos. 3,573,446, 3,581,199, 3,634,760, 3,881,097, 3,920,978, 4,607,216 and 4,686,457, some of which date back fifteen years and more.
The current state of the art is illustrated by the Hewlett-Packard HP-35660 Dynamic Signal Analyzer. Included in this and other comparable instruments is a Total Harmonic Distortion function that can determine the frequencies at which the harmonics of a fundamental signal should be found and can sum the spectral powers at these harmonics. The ratio of this sum to the signal's power at the fundamental frequency is a commonly used measure of the signal's total harmonic distortion.
Due to the use of the fast Fourier transform in such instruments, the signal spectrums analyzed are broken into discrete ranges of frequencies, termed "bins." The bandwidth of these bins is dependent on the length of the interval during which the instrument samples the signal. If the interval is very short, the component frequencies of the signal cannot be resolved very accurately and the bins are commensurately broad. As the interval is lengthened, resolution of the spectrum improves and bins narrow. For example, with a sampling interval of 3.90625 milliseconds and a sampling rate of 262,144 hertz, a spectrum resolution, or bin width, of 256 hertz is obtained.
To determine the total harmonic distortion (THD) of a signal, the frequency of the fundamental must first be known so that the frequencies of the harmonics can be determined and the signal components at these frequencies can be summed. In automated measurements of THD it is common practice to measure the spectrum and assume that the frequency component of largest amplitude is the fundamental. However, since FFT analyzers can only resolve the frequency of a signal to the width of one frequency bin, some assumption must be made as to the fundamental's precise frequency. In prior art automated analysis techniques, the assumption has typically been that the fundamental frequency is at the center of the bin with the maximum amplitude. This assumption is then used in determining which harmonic bins should be examined and summed to determine harmonic content of the signal.
If the fundamental frequency is not, in fact, at the center of the bin, the process will incorrectly calculate the frequencies at which the harmonics occur and may examine the wrong bins to determine the harmonic amplitudes. The wrong bins will not contain harmonics and will thus provide a misleadingly low indication of THD.
Consider, for example, a system in which the bin width is 256 hertz and the fundamental is at 2700 hertz. 2700 hertz is included in the 12th bin, which extends from 2688 to 2944 hertz with a center frequency of 2816. The deviation of the actual fundamental from the center of the bin is 116 hertz. In evaluating the harmonic distortion contributed by the eighth harmonic, the process would calculate the harmonic to be at (8*2816) or 22,528 hertz, which falls in the 89th bin. However, the actual harmonic is at (8*2700) or 21,600 hertz, which falls in the 85th bin. The amplitude of signals in the 89th bin, which is examined by the process in compiling THD, will normally be substantially less than the amplitude of signals in correct bin 85. The resulting THD measurement will thus be much lower than is actually the case.
If the analyzer is being operated by a skilled technician, this problem can be overcome. The default assumption that the fundamental is in the center of the largest amplitude bin can be overridden. The technician can enter the precise fundamental frequency, if it is known, on a data entry keypad on the instrument. Alternatively, he can adjust a vernier frequency control until harmonic marker signals displayed on the analyzer screen coincide with the harmonic spectral peaks in the signal being analyzed. However, these techniques require intervention of a skilled operator and are unsuitable for fully automated test and measurement applications.
A need remains for a technique that will permit accurate determinations of THD without intervention of a skilled operator.
According to the present invention, the accuracy of an automated THD measurement is improved by refining the estimate of the signal's fundamental frequency on which the THD analysis is based. This refinement is accomplished by calculating a parameter that represents the relative accuracy of the estimate and then varying the estimate to maximize the parameter. The result is a process which permits refinement of the fundamental frequency to an almost arbitrary accuracy, resulting in a highly improved, speed efficient measurement of THD.
The foregoing and additional objects, features and advantages of the present invention will be more readily apparent from the following detailed description thereof, which proceeds with reference to the accompanying drawings.